System and method for focal-plane angular-spatial illuminator/detector (fasid) design for improved graded index lenses

ABSTRACT

The present disclosure relates to a method for imaging an optical signal received by a graded index (GRIN) optical element to account for known variations in a graded index distribution of the GRIN optical element. The method may involve using a plurality of optical detector elements to receive optical rays received by the GRIN optical element at a plane, where the plane forms a part of the GRIN optical element or is downstream of the GRIN optical element relative to a direction of propagation of the optical rays. The optical rays are then traced to a plurality of additional specific locations on the plane based on the known variations in the graded index distribution of the GRIN optical element. A processor may be used to determine information on both an intensity and an angle of the received optical rays at each one of the plurality of specific locations on the plane of the GRIN optical element.

STATEMENT OF GOVERNMENT RIGHTS

The United States Government has rights in this invention pursuant toContract No. DE-AC52-07NA27344 between the U.S. Department of Energy andLawrence Livermore National Security, LLC, for the operation of LawrenceLivermore National Laboratory.

FIELD

The present disclosure relates to graded index (GRIN) optical elements,and more particularly to a system and method which enhances theperformance of a graded index element (such as a lens) based on ageometric optics transformation of a received optical signal at someoptical plane after the element (such as the focal plane of the lens).

BACKGROUND

The statements in this section merely provide background informationrelated to the present disclosure and may not constitute prior art.

Optical lens based systems are the backbone for many commercialapplications, e.g., imaging and directed illumination systems. At theheart of these systems is the lensing optical system. However, theoptical performance of an optical lensing system is limited byfabrication capabilities. For example, the ability to image at once thesky hemi-sphere for astronomical applications, which require wide anglecameras (such as for virtual reality applications), or to project lightfrom a planar emitter to the hemisphere or a selected area on thehemisphere for LIDAR (Light Detection and Ranging applications), arelimited by lensing design and fabrication methods for manufacturingfish-eye lenses.

For a fish-eye lens that projects the hemi-sphere on the lowerhemisphere of a Luneburg spherical lens, it was recently shown that thelens could be modified using transformation optics to project a skyhemi-sphere onto a plane (where a detector could be positioned at, forexample). However, such a device requires a graded-index (GRIN) opticswith large variations in index across the structure volume. This isproblematic because present day fabrication processes for GRIN opticsare limited in respect to the refractive index difference and spatialresolution, especially in the short wavelength range (i.e., nearinfra-red, visible, ultra-violet). Therefore, the performance of currenttechnology implementation for the manufacture of GRIN optics preventsthe use of such optics in important applications.

SUMMARY

In one aspect the present disclosure relates to a method for imaging anoptical signal received by a graded index (GRIN) optical element toaccount for known variations in a graded index distribution of the GRINoptical element. The method may comprise using a plurality of opticaldetector elements to receive optical rays received by the GRIN opticalelement at specific locations on a plane, where the plane forms a partof GRIN optical element or is downstream of the GRIN optical elementrelative to a direction of propagation of the optical rays. The methodmay further involve tracing received optical rays to a plurality ofadditional specific locations on the plane based on the known variationsin the graded index distribution of the GRIN optical element. Aprocessor may be used to determine information on both an intensity andan angle of the received optical rays at each one of the plurality ofspecific locations on the plane.

In another aspect the present disclosure relates to a method for imagingan optical signal received by a graded index (GRIN) optical element toaccount for known variations in a graded index distribution of the GRINoptical element. The method may comprise using a plurality of opticaldetector elements to receive optical rays received by the GRIN opticalelement at a plane of the GRIN optical element. The method may furtherinvolve using ray tracing software to analyze received optical rays andto map the received optical rays to a plurality of different, specificlocations on the plane of the GRIN optical element based on the knownvariations in the graded index distribution of the GRIN optical element.The method may further involve using a processor to calculate adistribution of both an intensity and an angle of the received opticalrays at each one of the plurality of specific locations on the plane ofthe GRIN optical element. The method may further involve modifying atleast one of the intensity and angle of the received optical rays, basedon the calculated distribution of the intensity and angle of thereceived optical rays, to account for the known variations in the gradedindex distribution of the GRIN optical element.

In still another aspect the present disclosure relates to a method forimaging an optical signal received by a graded index (GRIN) opticalelement to account for known variations in a graded index distributionof the GRIN optical element. The method may comprise using a pluralityof optical detector elements in the form of lenslets to receive opticalrays received by the GRIN optical element at a plurality of locations ona focal plane of the GRIN optical element. The method may furtherinvolve mapping the received optical rays to a plurality of different,specific locations on the focal plane of the GRIN optical element basedon the known variations in the graded index distribution of the GRINoptical element. The method may further involve using a processor tocalculate a distribution of both an intensity and an angle of thereceived optical rays at each one of the plurality of specific locationson the focal plane of the GRIN optical element. Still further, themethod may involve modifying both the intensity and angle of thereceived optical rays, based on the calculated distribution of theintensity and angle of the received optical rays, to account for theknown variations in the graded index distribution of the GRIN opticalelement.

Further areas of applicability will become apparent from the descriptionprovided herein. It should be understood that the description andspecific examples are intended for purposes of illustration only and arenot intended to limit the scope of the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings described herein are for illustration purposes only and arenot intended to limit the scope of the present disclosure in any way.

FIG. 1a illustrates a diagram showing how well known ray tracingsoftware is able to project how a light ray is bent as the light raytravels through a GRIN optical element that is designed to function as alens, where the refractive index distribution is known; where the lightrays emanated by two different point sources at the night sky areassigned different reference numbers; and where the GRIN optical elementwhich functions as a lens is focusing the different rays into differentlocations at its other end, which functions therefore as a focal plane;

FIG. 1b shows how the paths of a plurality of light rays emanating fromdifferent sources in the sky, and passing through an input surface of aplanar slab (e.g., planar lens) may be traced to specific locations onan output surface of the planar slab, where the slab has a known GRINdistribution, by using well known ray tracing software; for ideallyimplemented graded refractive index distribution, all the rays thatarrives from a given direction (i.e., given point source in the nightsky) are mapped uniquely onto the same location on the focal plane(i.e., output of the planar lens), which is represented in FIG. 1b onthe output location—angle (r₀−θ₀) plane as a straight line normal to ther₀ plane;

FIG. 1c shows a more accurate depiction of how in a real world,presently manufactured fish-eye lens, there will be an overlap of thelight rays entering at different points on an input surface the fish-eyelens when the light rays reach the output surface (i.e., the light rayswill not be perfectly focused at the same point on the output surface aswould be the case with a perfectly manufactured fish-eye lens);

FIG. 2 is a high level block diagram of one embodiment of a detectorsystem in accordance with the present disclosure for optimizing theperformance of an imperfect graded index (GRIN) lens; and

FIG. 3 is a high level flowchart illustrating major operations performedby the system of FIG. 2 in determining both the spatial and intensitydistribution of received optical rays on the focal plane of the GRINlens.

DETAILED DESCRIPTION

The following description is merely exemplary in nature and is notintended to limit the present disclosure, application, or uses. Itshould be understood that throughout the drawings, correspondingreference numerals indicate like or corresponding parts and features.

The present disclosure involves a method and system that enhances theperformance of an graded index (GRIN) optical element based on ageometric optics transformation of an optical signal at some designatedpoint of the element, for example on a focal plane of the element. At abroad level, in one example the present disclosure involvesmeasuring/manipulating the intensity and angle of the light spatially atthe focal plane (i.e., output surface) of the optical element (forexample the focal plane of a lens).

It will be appreciated that geometric optics principles rely on thelight ray vector at each point at some determined location on, orrelative to, an optical element. For the following discussion it will beassumed that the optical element is a lens, and the determined locationis a focal plane of the lens. Thus, the geometric optics principles canbe said to rely on the light ray vector at each point on the focalplane, namely, the location on the focal plane and the direction.Referring to FIG. 1a , a ray vector 10 is illustrated. Given the rayvector 10 at one location and the refractive index in space, representedby reference number 12, the ray trajectory 10 a could be determineduniquely, such as illustrated in FIG. 1a . This operation may be easilyaccomplished with ray-tracing commercial software (e.g., Code V opticaldesign software available from Synopsys of Mountain View, Calif., oroptical design software available from Zemax LLC) or by hand-writtencodes.

Referring to FIG. 1b , given an assumed GRIN distribution in a planarslab 14 functioning as an optical lens, the ray tracing software mapseach input light (i.e., optical) ray 16 a-16 e emanating from the samepoint in space, which enter an input surface 14 a of the planar slab 14,to a corresponding ray vector 18 a-18 e at an output surface 14 b of theplanar slab 14. Likewise, each light (i.e., optical) ray 17 a-17 eemanating from a different point in space is mapped to a different rayvector 19 a-19 e. For the planar slab 14 to function as an idealfish-eye lens, for example, all the input rays 18 a-18 e at the givenangle would need to map to one location 20 at the output surface 14 b,distinct from other input angles, and all the input rays 19 a-19 b wouldlikewise need to map to one location 21, which would be different fromlocation 20 in this example because the rays 16 a-16 e and 17 a-17 eoriginate from different points in space. However, for a non-idealizedfish-eye lens 14′ as shown in FIG. 1c , which has an input surface 14 a′and an output surface 14 b′, there will be an “overlap” on the outputsurface 14 b′ between these entrance angles for the rays 16 a-18 e. Putdifferently, the rays 16 a-16 e entering the input surface 14 a′ of thenon-idealized fish-eye lens 14′ will not be focused to the exact samespot on the focal plane (i.e., output surface) of the lens, but ratherwill be focused to different spots within a region 22 as shown by rays18 a-18 e. Region 22 illustrates this overlap.

The system and method of the present disclosure will now be describedwith reference to a detector system 100 shown in FIG. 2. The system 100enables detecting both the intensity and the angle of optical raysarriving at the output surface 14 b of the GRIN lens 14, where theoutput surface 14 b in this example is the focal plane. In this examplethe system 100 may make use of a plurality of optical detector elements,which in this example may be lenslets 102, which each cover apredetermined group of pixels 104 for detecting the presence of incomingrays 16 and 17. Typically hundreds, thousands or more of the lenslets102 may be incorporated in the system 100, depending on how many pixels104 are being used. The lenslets 102 are sufficient in number andarranged to preferably image the entire output surface 14 b (i.e., theentire focal plane) of the GRIN lens 14. The system 100 also may includea processor 106 which receives signals from the lenslets 102 and whichalso communicates with a memory 108. The memory 108 may be anon-volatile memory that includes one or more algorithms 110 forcarrying out the diagonalization of a linear system matrix using theinformation supplied from the lenslets 102.

As explained with reference to FIG. 1c , for the imperfect GRIN lens 14,when exciting the lens 14 with each of the different entrance angles forrays 16 and 17 on all of the input surface 14 a (i.e., entrance)locations of the lens, this will result in a distinctive spatial-angularoutput distribution. Performing a correlation between the obtaineddistribution of entrance angles of the rays 16 and 17 entering the lens14, and the distinctive pattern for each entrance angle, enables amaximal value to be obtained for each excitation angle of optical raythat excited the lens 14. For received light rays that produce multipleexcitation angles (a result of multiple objects on the sky hemi-sphere),there will be multiple correlation maximum locations at thecorresponding distribution matching the exciting angles, since thesystem 100 is a linear system. Put differently, for the example shown inFIG. 2, since there are rays entering the lens 14 at two distinctentrance angles (i.e., rays 16 and 17 shown entering the lens atdifferent angles), this will produce two correlation maximum spatiallocations on the lens output surface 14 b: one for the rays 16 andanother for the rays 17. This operation may be described mathematicallyas diagonalization of the linear system matrix, and the algorithms fordiagonalization of the linear system matrix 110, stored in memory 108,are used by the processor 106 to carry out this diagonalization. As thelens 14 would be close to a perfect fish-eye lens, the overlap of thedifferent input angle cases would be smaller, enabling better separationresolution over larger night sky angle. The GRIN lens refractive indexdistribution and the algorithm is then optimized to minimize the overlapof different input angles (i.e., minimize the r₀ width of thedistribution in FIG. 1c ). Optimization of the GRIN lens distributionand the transformation algorithm by the system 100, under thefabrication constraints of the optics and required specifications, isexpected to result in improved performance of the lens 14 due to theadditional degrees of freedom allowed in the construction of the lens.This principle, demonstrated here for a GRIN optical element that formsa GRIN optical lens (using the spatial-angular information at the focalplane), could be implemented to improve the performance of other GRINoptical elements constrained by fabrication limitations using thespatial-angular information at a plane after (i.e., downstream relativeto the direction of the rays 16 and 17) the element (e.g., spectroscopicgratings).

As noted above, the detector system 100 is able to record the angulardistribution of light rays (which includes both angle and intensity)that are received by the lens 14 at a large plurality of locations onthe output surface 14 b of the lens, and more preferably at everylocation on the output surface (i.e., focal plane) of the lens 14. Thegroup of light rays that arrive at a specific lenslet 102 location isseparated by the different pixels associated with that particularlenslet, according to the arriving directions (i.e., arriving angles ofeach light ray imaged by each pixel). Therefore, the intensity at aspecific focal plane location (i.e., specific location on the outputsurface 14 b) is the sum of all the rays arriving at that particularlenslet 102, and the angular distribution is determined by the sub-pixellocation for this lenslet. The ratio between the focal length of thelenslet 102 and the spatial deviation from the lenslet center gives theangle of the incoming ray(s) received at a given lenslet 102.

Referring to FIG. 3, a high level flowchart 200 is shown illustratingmajor operations performed in carrying out the methodology of thepresent disclosure. At operation 202 the lenslets 102 are used toreceive the optical rays 16 and 17 being imaged by the GRIN lens 14. Atoperation 204, suitable ray tracing software may be used to map incomingoptical rays 166 and 17 to specific locations on the output surface 14 b(i.e., focal plane) of the GIN lens 14. At operation 206 the processor106 applies the algorithm(s) 108 to calculate the diagonalization of thelinear system matrix to predict the sources (i.e., point sources at thenight sky) that resulted in the detected spatial-angular distribution onthe detector. At operation 208, the operations for determining the GRINoptical element refractive index distribution and diagonalization arenow complete, and such operations may be concluded. Based on the processdescribed from “Start” to operation 206 (being the output) for a GRINoptical element with different refractive index distribution, anoptimization step, as indicated by operation 210 may then be executedwhich changes the index distribution and seeks to maximize theseparation between distinctive sources' output distributions.

The methodology disclosed herein also holds for other imaging systemsand also to illumination systems. For an illumination system, the system100 may be modified to determine the focal plane illuminator profile,and combine requirements from the GRIN optics and the location and angledistribution of the source optical signal in order to generate anoptical signal having a desired spatial/intensity profile. A spatialcontrol of the angle(s) of optical signals projected could also beachieved with micro-MEMS system, for example. A similar approach foroptimizing the fabrication-limited function of the GRIN lens may useadditional degrees of freedom (e.g., emitters' locations, brightnessesand GRIN lens index) for tailoring specialized irradiation patterns.

While various embodiments have been described, those skilled in the artwill recognize modifications or variations which might be made withoutdeparting from the present disclosure. The examples illustrate thevarious embodiments and are not intended to limit the presentdisclosure. Therefore, the description and claims should be interpretedliberally with only such limitation as is necessary in view of thepertinent prior art.

Example embodiments are provided so that this disclosure will bethorough, and will fully convey the scope to those who are skilled inthe art. Numerous specific details are set forth such as examples ofspecific components, devices, and methods, to provide a thoroughunderstanding of embodiments of the present disclosure. It will beapparent to those skilled in the art that specific details need not beemployed, that example embodiments may be embodied in many differentforms and that neither should be construed to limit the scope of thedisclosure. In some example embodiments, well-known processes,well-known device structures, and well-known technologies are notdescribed in detail.

The terminology used herein is for the purpose of describing particularexample embodiments only and is not intended to be limiting. As usedherein, the singular forms “a,” “an,” and “the” may be intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. The terms “comprises,” “comprising,” “including,” and“having,” are inclusive and therefore specify the presence of statedfeatures, integers, steps, operations, elements, and/or components, butdo not preclude the presence or addition of one or more other features,integers, steps, operations, elements, components, and/or groupsthereof. The method steps, processes, and operations described hereinare not to be construed as necessarily requiring their performance inthe particular order discussed or illustrated, unless specificallyidentified as an order of performance. It is also to be understood thatadditional or alternative steps may be employed.

When an element or layer is referred to as being “on,” “engaged to,”“connected to,” or “coupled to” another element or layer, it may bedirectly on, engaged, connected or coupled to the other element orlayer, or intervening elements or layers may be present. In contrast,when an element is referred to as being “directly on,” “directly engagedto,” “directly connected to,” or “directly coupled to” another elementor layer, there may be no intervening elements or layers present. Otherwords used to describe the relationship between elements should beinterpreted in a like fashion (e.g., “between” versus “directlybetween,” “adjacent” versus “directly adjacent,” etc.). As used herein,the term “and/or” includes any and all combinations of one or more ofthe associated listed items.

Although the terms first, second, third, etc. may be used herein todescribe various elements, components, regions, layers and/or sections,these elements, components, regions, layers and/or sections should notbe limited by these terms. These terms may be only used to distinguishone element, component, region, layer or section from another region,layer or section. Terms such as “first,” “second,” and other numericalterms when used herein do not imply a sequence or order unless clearlyindicated by the context. Thus, a first element, component, region,layer or section discussed below could be termed a second element,component, region, layer or section without departing from the teachingsof the example embodiments.

Spatially relative terms, such as “inner,” “outer,” “beneath,” “below,”“lower,” “above,” “upper,” and the like, may be used herein for ease ofdescription to describe one element or feature's relationship to anotherelement(s) or feature(s) as illustrated in the figures. Spatiallyrelative terms may be intended to encompass different orientations ofthe device in use or operation in addition to the orientation depictedin the figures. For example, if the device in the figures is turnedover, elements described as “below” or “beneath” other elements orfeatures would then be oriented “above” the other elements or features.Thus, the example term “below” can encompass both an orientation ofabove and below. The device may be otherwise oriented (rotated 90degrees or at other orientations) and the spatially relative descriptorsused herein interpreted accordingly.

What is claimed is:
 1. A method for imaging an optical signal receivedby a graded index (GRIN) optical element to account for known variationsin a graded index distribution of the GRIN optical element, the methodcomprising: using a plurality of optical detector elements to receiveoptical rays received by the GRIN optical element at specific locationson a plane, where the plane forms a part of GRIN optical element or isdownstream of the GRIN optical element relative to a direction ofpropagation of the optical rays; tracing received optical rays to aplurality of additional specific locations on the plane based on theknown variations in the graded index distribution of the GRIN opticalelement; and using a processor to determine information on both anintensity and an angle of the received optical rays at each one of theplurality of specific locations on the plane.
 2. The method of claim 1,further comprising using the information on both the intensity and theangle of received optical rays at each one of the plurality of specificlocations on the plane to generate a correction for at least one of theangle and intensity to account for the variation in the graded index ofthe GRIN optical element.
 3. The method of claim 1, wherein using theplurality of optical detector elements comprises using a plurality oflenslets.
 4. The method of claim 3, wherein using a plurality oflenslets comprises using a plurality of lenslets sufficient in numberand arranged to cover an entire area of the plane.
 5. The method ofclaim 3, wherein using the plurality of lenslets comprises using eachone of the plurality of lenslets to receive signals from a plurality ofassociated pixels.
 6. The method of claim 1, wherein using a processorto determine information on both an intensity and an angle of thereceived optical rays comprises using the processor to run an algorithmfor calculating a diagonalization of a linear system matrix using theinformation.
 7. The method of claim 1, wherein tracing received opticalrays to specific locations on the focal plane of the GRIN opticalelement comprises using optical ray tracing software to map optical raysreceived at an input surface of the GRIN optical element to a focalplane of the GRIN optical element.
 8. The method of claim 1, whereinusing a plurality of optical detector elements to receive optical raysreceived by the GRIN optical element comprises using a plurality ofoptical detector elements to receive optical rays received by a GRINoptical element.
 9. A method for imaging an optical signal received by agraded index (GRIN) optical element to account for known variations in agraded index distribution of the GRIN optical element, the methodcomprising: using a plurality of optical detector elements to receiveoptical rays received by the GRIN optical element at a plane of the GRINoptical element; using ray tracing software to analyze received opticalrays and to map the received optical rays to a plurality of different,specific locations on the plane of the GRIN optical element based on theknown variations in the graded index distribution of the GRIN opticalelement; using a processor to calculate a distribution of both anintensity and an angle of the received optical rays at each one of theplurality of specific locations on the plane of the GRIN opticalelement; and modifying at least one of the intensity and angle of thereceived optical rays, based on the calculated distribution of theintensity and angle of the received optical rays, to account for theknown variations in the graded index distribution of the GRIN opticalelement.
 10. The method of claim 9, wherein using a plurality of opticaldetector elements comprises using a plurality of lenslets.
 11. Themethod of claim 10, wherein using a plurality of lenslets comprisesusing a plurality of lenslets sufficient in number to cover an entirearea of the plane of the GRIN optical element.
 12. The method of claim10, wherein using a plurality of lenslets comprises using a plurality oflenslets each being associated with an associated plurality of pixels,and wherein the pixels associated with each said lenslet receive theoptical rays at the focal plane of the GRIN optical element.
 13. Themethod of claim 10, wherein using a plurality of lenslets comprisesusing a plurality of lenslets sufficient in number to cover an entirearea of a focal plane of the GRIN optical element.
 14. The method ofclaim 13, wherein covering an entire area of a focal plane of the GRINoptical element comprises covering an entire area of a GRIN lens.
 15. Amethod for imaging an optical signal received by a graded index (GRIN)optical element to account for known variations in a graded indexdistribution of the GRIN optical element, the method comprising: using aplurality of optical detector elements in the form of lenslets toreceive optical rays received by the GRIN optical element at a pluralityof locations on a focal plane of the GRIN optical element; mapping thereceived optical rays to a plurality of different, specific locations onthe focal plane of the GRIN optical element based on the knownvariations in the graded index distribution of the GRIN optical element;using a processor to calculate a distribution of both an intensity andan angle of the received optical rays at each one of the plurality ofspecific locations on the focal plane of the GRIN optical element; andmodifying both the intensity and angle of the received optical rays,based on the calculated distribution of the intensity and angle of thereceived optical rays, to account for the known variations in the gradedindex distribution of the GRIN optical element.
 16. The method of claim15, wherein mapping the received optical rays comprises using raytracing software to map the optical rays.
 17. The method of claim 15,wherein using a plurality of optical detector elements in the form oflenslets comprises using a plurality of lenslets sufficient in number toimage an entire focal plane of the GRIN optical element, and where theGRIN optical element forms a GRIN lens.
 18. The method of claim 17,wherein each said lenslet is associated with a plurality of pixels, andwherein the pixels receive the optical rays.